=== NPC Reason — Dispatch 2: V4 Corpus + SFT Distill ===

Corpus:   13,245 V4 (deepseek-v4-flash) chains from TRAIN splits (GSM8K-train + MATH-train 7 subj)
          -> mechanically filtered against FROZEN verifier (verifiable AND correct)
          -> 7,546 kept (keep rate 56.97%). TRAINSET.lock frozen.
          reject breakdown: no_assertions 3894 (29%, mostly non-arithmetic MATH) ·
          bad_arithmetic 1211 (9%) · non_composing 387 · wrong_answer 206 · dup 1
          decontam vs EVAL.lock: 0 overlap (train/test disjoint by construction)
          Finding: the strong teacher emits ungrounded/wrong chains ~43% of the time on this
          distribution; all rejected before training (the strict-basis move).

SFT:      R1-Distill-1.5B + LoRA r64 (7 modules, 73.9M = 3.99% trainable), batch1 x accum16,
          3 epochs, seq 1024 constant-pad (0.03% truncated), sdpa + gradient checkpointing.
          train loss 0.538 -> 0.075, eval 0.311, runtime 2h31m. Merged model saved (3.5GB).

Result:   (format-prompt, vs frozen baseline, greedy, frozen verifier)
          verifiable 76.8% (base 0.0) · accuracy 65.8% (base 61.6) · verified+correct 58.0% (base 0.0)
          mean assertions/chain 3.44 (base 0.0)

PREREG:   lift +58.0pp verified-and-correct  -> SUPPORTED (bar +15pp)
          verifiable-rate 76.8%               -> NOT SUPPORTED (bar 90%)
          accuracy delta +4.2pp (improved)    -> SUPPORTED (bar: no regress >5pp)
          => 2 of 3 SUPPORTED; all-three gate not met.

RL gate:  WARRANTED via the high-signal condition (76.8% verifiable / 58% v&c gives the
          verifier-reward RL dense signal); all-three bar NOT cleared (verifiable < 90 is the
          explicit RL target). Not a null — a large real lift missing one of three bars.

Honest:   Thesis validated — distilling ONLY verifier-confirmed chains took the model from 0%
          mechanically-checkable reasoning to 76.8% verifiable / 58% verified-and-correct, with
          accuracy rising not falling. The grounding transferred; the remaining ~23% unverifiable
          tail is the RL phase's job.

Decisions np-007..np-010 · all frozen locks intact · eval decontaminated · SFT_RESULT.lock frozen
Next:     Dispatch 3 = RLVR/GRPO with the frozen verifier as reward, target verifiable-rate >=90%,
          RL criteria pre-registered against a held-out slice never used for SFT selection.